Pith Number

pith:YT6LKM72

pith:2026:YT6LKM72OB63CFWTYKNZ7UK2D4

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Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group

Ariyan Javanpeykar, Benson Farb, Gregorio Baldi, Matthew Stover

The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.

arxiv:2605.16658 v1 · 2026-05-15 · math.AG · math.GR · math.GT

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Claims

C1strongest claim

We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.

C2weakest assumption

The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions.

C3one line summary

The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.

References

15 extracted · 15 resolved · 0 Pith anchors

[1] D. Allcock, J. A. Carlson, and D. Toledo. The complex hyperbolic geometry of the moduli space of cubic surfaces. J. Algebr. Geom., 11(4):659–724, 2002 2002

[2] D. Allcock, J. A. Carlson, and D. Toledo. Orthogonal complex hyperbolic arrangements. In Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) , volume 312 of Contemp. Math. , pages 1–8. Amer 2000

[3] W. L. Baily, Jr. and A. Borel. On the compactification of arithmetically defined quotients of bounded symmetric domains. Bull. Amer. Math. Soc. , 70:588–593, 1964 1964

[4] W. Bosma, J. Cannon, and C. Playoust. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4):235–265, 1997. Computational algebra and number theory (London, 1993) 1997

[5] M. R. Bridson and A. Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren Math. Wiss. Berlin: Springer, 1999 1999

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:34.838309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138

Aliases

arxiv: 2605.16658 · arxiv_version: 2605.16658v1 · doi: 10.48550/arxiv.2605.16658 · pith_short_12: YT6LKM72OB63 · pith_short_16: YT6LKM72OB63CFWT · pith_short_8: YT6LKM72

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YT6LKM72OB63CFWTYKNZ7UK2D4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c4fcb533fa707db116d3c29b9fd15a1f3e25dcf8e590d53f8de09681559e5138

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45c53f09fcd6fc1303888c4b34b48f6d728fdb632e4fb5c799f2270f4838f68e",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-15T21:54:13Z",
    "title_canon_sha256": "556076b848477cd5735e14086083fd85e15446db6a1d14a5fc06a47a418a6059"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16658",
    "kind": "arxiv",
    "version": 1
  }
}